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Elongated Square Dipyramid
In geometry, the elongated square bipyramid (or elongated octahedron) is one of the Johnson solids (). As the name suggests, it can be constructed by elongating an octahedron by inserting a cube between its congruent halves. It has been named the pencil cube or 12-faced pencil cube due to its shape.Order in Space: A design source book, Keith Critchlow, p.46-47 A zircon crystal is an example of an elongated square bipyramid. Formulae The following formulae for volume (V), surface area (A) and height (H) can be used if all faces are regular, with edge length L: :V = L^3\cdot \left( 1 + \frac\right) \approx L^3\cdot 1.471404521 :A = L^2\cdot \left(4 + 2\sqrt\right) \approx L^2\cdot 7.464101615 :H = L\cdot \left( 1 + \sqrt\right) \approx L\cdot 2.414213562 Dual polyhedron The dual of the elongated square bipyramid is called a square bifrustum and has 10 faces: 8 trapezoidal and 2 square. Related polyhedra and honeycombs A special kind of elongated square bipyramid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johnson Solid
In geometry, a Johnson solid is a strictly convex polyhedron each face of which is a regular polygon. There is no requirement that isohedral, each face must be the same polygon, or that the same polygons join around each Vertex (geometry), vertex. An example of a Johnson solid is the square-based Pyramid (geometry), pyramid with equilateral sides (square pyramid, ); it has 1 square face and 4 triangular faces. Some authors require that the solid not be uniform polyhedron, uniform (i.e., not Platonic solid, Archimedean solid, prism (geometry), uniform prism, or uniform antiprism) before they refer to it as a “Johnson solid”. As in any strictly convex solid, at least three faces meet at every vertex, and the total of their angles is less than 360 degrees. Since a regular polygon has angles at least 60 degrees, it follows that at most five faces meet at any vertex. The pentagonal pyramid () is an example that has a degree-5 vertex. Although there is no obvious restriction tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
